In another problem, we saw that in an isosceles triangle, the height to the base from the apex is also the angle bisector. Here, we will show the opposite: that the angle bisector is perpendicular to … [Read more...] about Angle bisector is perpendicular to the base in an isosceles triangle
Isosceles Triangle
A triangle in which two of the sides are equal is called an “Isosceles triangle”, and we often identify the equal side by tagging them with a short line:
The third side is called the "base", and we will prove that the angels at the two sides of the base (and opposite the two equal sides) are congruent.
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Now that we've explained the basic concept of isosceles triangles in geometry, let's scroll down to work on specific geometry problems relating to this topic.
Converse Base Angle Theorem
In today's lesson, we will prove the converse to the Base Angle theorem - if two angles of a triangle are congruent, the triangle is isosceles. We will use congruent triangles for the proof. From … [Read more...] about Converse Base Angle Theorem
Angle Bisector in a Triangle
Today's geometry problem presents an application of the angle bisector theorem in a triangle. It also incorporates several other concepts we've explored, like the properties of isosceles triangles and … [Read more...] about Angle Bisector in a Triangle
Converse Angle Bisector Theorem for Isosceles Triangles
In today's lesson, we will prove the Converse Angle Bisector Theorem for Isosceles Triangles. We'll show that if a triangle's angle bisector is perpendicular to the opposite side, the triangle is an … [Read more...] about Converse Angle Bisector Theorem for Isosceles Triangles
Isosceles Triangles: the Median to the Base is Perpendicular to the Base
In a triangle, a line that connects one corner (or vertice) to the middle point of the opposite side is called a median. A property of isosceles triangles, which is simple to prove using triangle … [Read more...] about Isosceles Triangles: the Median to the Base is Perpendicular to the Base
Isosceles Triangles: the Height to the Base Bisects the Apex Angle
We can use the proof that in isosceles triangles the height to the base bisects the base, and get a "two-for-one," as the exact same proof shows us multiple corresponding parts that are … [Read more...] about Isosceles Triangles: the Height to the Base Bisects the Apex Angle
The Height to the Base of an Isosceles Triangle Bisects the Base
In today's lesson we'll learn a simple strategy for proving that in an isosceles triangle, the height to the base bisects the base. Having proven the Base Angles Theorem for isosceles triangles … [Read more...] about The Height to the Base of an Isosceles Triangle Bisects the Base
Base Angles Theorem
In this lesson, we will show you how to easily prove the Base Angles Theorem: that the base angles of an isosceles triangle are congruent. We will prove most of the properties of special triangles … [Read more...] about Base Angles Theorem